Roman Polanski’s arrest coincides with the 35th anniversary of the di rector’s greatest film, “Chinatown,” released three years before he fled the United States after pleading guilty to having sex with a 13-year-old girl.

“Chinatown,” just out in a new DVD edition from Paramount, of course stars Jack Nicholson, in whose home Polanski’s crime occurred (the actor was not there), and climaxes with the aftermath of a horrific sexual act involving a minor.

As John Huston’s decadent character chillingly puts it, “Most people never have to face the fact that at the right time and the right place they’re capable of anything.”

Nicholson plays a disgraced private detective in 1937 Los Angeles, hired to trail a water commissioner suspected of infidelity, who stumbles on a couple of much larger scandals.

Polanski has a memorable cameo as a gangster who slits Nicholson’s nostril to discourage his snooping. In a 2007 making-of documentary included on the DVD, Polanski says he resisted Nicholson’s and producer Robert Evans’

demand he play the part because Polanski didn’t want to cut his long hair.

Polanski also says he can’t imagine that a Hollywood studio today would agree to have a big star wear a large bandage through much of the movie, as Nicholson does.

The director recounts a heated argument he had with the movie’s female lead, Faye Dunaway, when he yanked out one of her stray hairs that the film’s hairdresser was having trouble getting under control.

But Polanski says Dunaway encouraged him to order Nicholson to actually hit her — rather than fake it — in the famous confrontation scene in which he’s trying to determine whether a young girl is Dunaway’s daughter or sister.

The DVD includes a new hourlong documentary on Los Angles’ water-supply system, which uses aqueducts to pipe in water from hundreds of miles away in the Sierra Nevada mountains.

The famously convoluted plot of “Chinatown” was inspired by real-life dirty deals involving the water — although screenwriter Robert Towne admits he never actually visited the reservoir system until earlier this year.